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<h1>If Estimation
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>INSTANTANEOUS FREQUENCY ESTIMATION</strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="fragment"><pre class="comment"> INSTANTANEOUS FREQUENCY ESTIMATION

 Includes different methods to estimate the instantaneous frequency
 for given time-domain signal

 These different techniques include:

   (i)    Finite Phase Difference
   (ii)   Weighted Phase Difference
   (iii)  Zero-Crossing
   (iv)   Adaptive Estimators
   (v)    Least Squares
   (vi)   Peak of Spectrogram
   (vii)  Peak of Wigner-Ville Distribution
   (viii) Peak of Polynomial Wigner-Ville Distribution

   PARAMETERS:

   SIGNAL
        
       One dimensional input signal.
   
   ESTIMATED FREQUENCY ARRAY
   
       One dimensional output signal containing the estimated
       instantaneous frequency (IF) law for given input signal.


   EXPLANATION OF VARIOUS TECHNIQUES:
  
   (i) Finite Phase Difference

       Estimates the IF law of the input signal using the general
       phase difference method. Only first, second, fourth and sixth
       order phase difference estimators are available in the case
       when no smoothing is required. The signal phase is unwrapped
       when a fourth or a sixth order estimator is applied

   (ii) Weighted Phase Difference

       This function uses the Kay weighted difference estimator. A
       sliding Kay window is used to smooth the phase. The local
       smoothed estimate inside the moving quadratic window is
       computed each time the window moves.  

   (iii) Zero Crossings

       Estimates the IF law of the input signal using the
       zero-crossing estimation algorithm. It estimates the frequency
       by taking the average number of zero-crossings within a
       sliding window.

   (iv) Adaptive Estimators

       Two methods can be selected here, the least mean square (LMS)
       adaptive IF estimator and the recursive least square (RLS)
       adaptive IF estimator.  The LMS method is based on a single
       tap linear prediction filter which has its coefficients
       updated as each new data sample is received. The positive
       adaptation constant controls the rate adaptation. The RLS
       method is based on a single tap linear prediction filter which
       has its coefficients updated as each new data sample is
       received. The forgetting factor controls the rate of
       adaptation. Both the adaptation constants must be positive.

   (v) Least Squares 

       Estimates the IF law of the input signal by obtaining the
       phase of the input signal and then fitting a polynomial. The
       order of the polynomial is selected using the parameter
       order. The order of the polynomial to be fitted to the can be
       specified.

   (vi) Peak of Spectrogram

       Estimates the IF law of the input signal using the peak of the
       spectrogram method. SEE ALSO: spec

   (vii) Peak of Wigner-Ville Distribution

       Estimates the IF law of the input signal using the peak of the
       Wigner-Ville distribution method. SEE ALSO: wvd

   (viii) Peak of Polynomial Wigner-Ville Distribution

       Peak of the sixth order polynomial Wigner-Ville distribution
       IF estimation algorithm. SEE ALSO: pwvd6</pre></div>

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